The necessary conditions for (normal) efficient solutions to a class of multiobjective fractional variational problems (MFP) with nonlinear equality and inequality constraints are established using a parametric approach to relate efficient solutions of a fractional problem and a non-fractional problem. | Yugoslav Journal of Operations Research Vol 19 (2009), Number 1, 85-99 DOI: EFFICIENCY AND DUALITY FOR MULTIOBJECTIVE FRACTIONAL VARIATIONAL PROBLEMS WITH ( ρ , b) QUASIINVEXITY Ştefan MITITELU Technical University of Civil Engineering, Bucharest, Romania st_mititelu@ I. M. STANCU-MINASIAN ”Gheorghe Mihoc-Caius Iacob” Institute of Mathematical Statistics and Applied Mathematics, Bucharest, Romania stancu_minasian@ Received: December 2007 / Accepted: June 2009 Abstract. The necessary conditions for (normal) efficient solutions to a class of multiobjective fractional variational problems (MFP) with nonlinear equality and inequality constraints are established using a parametric approach to relate efficient solutions of a fractional problem and a non-fractional problem. Based on these normal efficiency criteria a Mond-Weir type dual is formulated and appropriate duality theorems are proved assuming ( ρ , b) - quasi-invexity of the functions involved. Keywords: Duality, fractional variational problem,quasi-invexity. 1. INTRODUCTION For the first results on the necessity of the optimal solutions of the variational problems we cite the Valentine’s paper[17]. The papers of Mond and Hanson [9, 10], Bector [1], Mond, Chandra and Husain [12], Mond and Husain [11], Smart and Mond [16] and Preda [14] developed the duality of the scalar variational problems involving convex and generalized convex functions. Mukherjee and Purnachandra [13], Preda and Gramatovici [15] and Mititelu [7] established weak efficiency conditions and developed 86 Ş. Mititelu, . Stancu-Minasian / Eficiency And Duality different types of dualities for multiobjective variational problems generated by various types of generalized convex functions. Kim and Kim [4] used the efficiency property of the multi-objective variational problems in the duality theory. In this paper we will introduce the notion of normal efficient solution and establish the necessary .
